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A stochastic model of an information channel with random intensities and random loads is constructed. We investigate a model of an information flow in which some part of information from "the past" is projected to "the present" and another part of the information is left behind. The "present" information is supplemented by some innovations which replace the vanished information. We obtain several limit theorems for normed sums of independent identically distributed information channels. A class of limit processes consists of various generalizations of the Ornstein–Uhlenbeck process. We also describe a construction of self-similar processes with a wide range of one-dimensional distributions of their truncations. [ABSTRACT FROM AUTHOR]

We investigated the anomalous diffusion in a system of N–Brownian particles connected by spring driven by one-parameter Mittag-Leffler noise. We presented a solution to the generalized Langevin equation and derived exact expressions for the diffusion coefficient and the variances of the phase space variables of the ith particle in the chain in terms of the Rouse modes. Our results show that all the particles in the linear chain observe subdiffusion. In the limit approaching the Ornstein-Uhlenbeck process, the particles observe normal diffusion indicated by a constant value of the diffusion coefficient in the long-time limit. [ABSTRACT FROM AUTHOR]

Bilateral Laplace transform is known for its capability on taking Laplace transform over all real numbers. This paper provides a different approach by using inverse bilateral Laplace transform on deriving analytic solution of European option price formula, both call option and put option. Case of uncorrelated processes between asset price and volatility of Black-Scholes model of asset pricing with stochastic volatility driven by Ornstein-Uhlenbeck process is used to portray price of a risky asset in the market. This paper also provides proof for required formulations to derive the analytic solutions and reference for alternative forms of inverse bilateral Laplace transform. [ABSTRACT FROM AUTHOR]

Stochastic volatility models are a variance extension of the classical Black-Scholes model dynamics by introducing an-other auxiliary processes to model the volatility of the underlying asset returns. Here we study the pricing problem for European-style options under a one-factor stochastic volatility model when the volatility of the underlying price is governed by the exponen-tial Ornstein–Uhlenbeck process. The problem can be formulated as a non-stationary second-order degenerate partial differential equation accompanied by initial and boundary conditions, whose analytical solutions are not available in general. Therefore, the approximate option value is obtained by a numerical procedure based on a discontinuous Galerkin technique that provides promising results. Finally, reference numerical experiments are provided with the emphasis on the behaviour of the option values with respect to the discretization parameters. [ABSTRACT FROM AUTHOR]

The Wilkie model is a stochastic asset model, developed by A.D Wilkie in 1984 with the purpose to explore the behavior of investment factors of insurer within the United Kingdom. The Wilkie model was considered as a discrete-time horizon model and we then reviewed the continuous time case which was initially introduced by Terence Chan in 1998. We comprehensively explain all four sub models in the Wilkie model and make comparison with the original Wilkie model in discrete time. Prior to that, we also discuss the famous Ornstein-Uhlenbeck process which will be used to develop the continuous-time Wilkie model. [ABSTRACT FROM AUTHOR]

In recent years, modeling in long memory properties or fractionally integrated processes in stochastic volatility has been applied in the financial time series. A time series with structural breaks can generate a strong persistence in the autocorrelation function, which is an observed behaviour of a long memory process. This paper considers the structural break of data in order to determine true long memory time series data. Unlike usual short memory models for log volatility, the fractional Ornstein-Uhlenbeck process is neither a Markovian process nor can it be easily transformed into a Markovian process. This makes the likelihood evaluation and parameter estimation for the long memory stochastic volatility (LMSV) model challenging tasks. The drift and volatility parameters of the fractional Ornstein-Unlenbeck model are estimated separately using the least square estimator (lse) and quadratic generalized variations (qgv) method respectively. Finally, the empirical distribution of unobserved volatility is estimated using the particle filtering with sequential important sampling-resampling (SIR) method. The mean square error (MSE) between the estimated and empirical volatility indicates that the performance of the model towards the index prices of FTSE Bursa Malaysia KLCI is fairly well. [ABSTRACT FROM AUTHOR]

Recently, a universal portfolio generated by a set of independent Brownian motions where a finite number of past stock prices are weighted by the moments of the multivariate normal distribution is introduced and studied. The multivariate normal moments as polynomials in time consequently lead to a constant rebalanced portfolio depending on the drift coefficients of the Brownian motions. For a weakly stationary process, a different type of universal portfolio is proposed where the weights on the stock prices depend only on the time differences of the stock prices. An empirical study is conducted on the returns achieved by the universal portfolios generated by the Ornstein-Uhlenbeck process on selected stock-price data sets. Promising results are demonstrated for increasing the wealth of the investor by using the weakly-stationary-process-generated universal portfolios. [ABSTRACT FROM AUTHOR]

This paper studies the Ornstein-Uhlenbeck model that incorporates long memory stochastic volatility which is known as fractional Ornstein-Uhlenbeck model. The determination of the existence of long range dependence of the index prices of FTSE Bursa Malaysia KLCI is measured by the Hurst exponent. The empirical distribution of unobserved volatility is estimated using the particle filtering method. The performance between fractional Ornstein -Uhlenbeck and standard Ornstein -Uhlenbeck process had been compared. The mean square errors of the fractional Ornstein-Uhlenbeck model indicated that the model describes index prices better than the standard Ornstein-Uhlenbeck process. [ABSTRACT FROM AUTHOR]

The paper proposes the characterization of frequency variations of the Irish grid in terms of stochastic differential equations. With this aim, the frequency is measured using a Frequency Disturbance Recorder lent to the first author by the University of Tennessee. Large sets of time series of frequency measurements are analysed and different scenarios based on wind and load levels are considered. Then, for each scenario the statistical properties of the frequency as well as the stochastic distribution that best fits the data are determined. Finally, the parameters determined on measured data are used to define synthetic stochastic differential equations that reproduce the behaviour of the frequency. A comprehensive discussion on main assumptions and simplifications is also provided in the paper. [ABSTRACT FROM AUTHOR]

A new tool, in the blind deconvolution, for the estimation of both the source signals and the unknown channel dynamics has been developed. The framework for this methodology is based on a multi-channel blind deconvolution technique that has been reformulated to use Stochastic Calculus. The convolution processes is modeled as Finite Impulse Response (FIR) filters with unknown coefficients. Assuming that one of the FIR filter coefficients is time-varying, we have been able to get accurate estimation results for the source signals, even though the filter order is unknown. The time-varying filter coefficient was assumed to be a stochastic process. A stochastic differential equation (SDE), with some unknown parameters, was developed that described its evolution over time. The SDE parameters have been estimated using methods in stochastic calculus. The method was applied to the problem of two chatting persons and the problem of EEG contaminated by EOG. Comparisons to existing methods are also reported. [ABSTRACT FROM PUBLISHER]

Market making refers broadly to trading strategies that seek to profit by providing liquidity to other traders, while avoiding accumulating a large net position in a stock. In this paper, we study the profitability of market making strategies in a variety of timeseries models for the evolution of a stock's price. We first provide a precise theoretical characterization of the profitability of a simple and natural market making algorithm in the absence of any stochastic assumptions on price evolution. This characterization exhibits a trade-off between the positive effect of local price fluctuations and the negative effect of net price change. We then use this general characterization to prove that market making is generally profitable on mean reverting time series --- time series with a tendency to revert to a long-term average. Mean reversion has been empirically observed in many markets, especially foreign exchange and commodities. We show that the slightest mean reversion yields positive expected profit, and also obtain stronger profit guarantees for a canonical stochastic mean reverting process, known as the Ornstein-Uhlenbeck (OU) process, as well as other stochastic mean reverting series studied in the finance literature. We also show that market making remains profitable in expectation for the OU process even if some realistic restrictions on trading frequency are placed on the market maker. [ABSTRACT FROM AUTHOR]

Based on vertical movement data derived from electronic storage tags (DST) attached to fish, we construct a stochastic model that aims at capturing the main characteristics of the observations over one year. We use a mixed Ornstein-Uhlenbeck process to model attraction to a limited number of concentration points on the depth axis. A methodology for determining states and transition probabilities between them, and for setting model parameters for the process, is discussed. We show some examples of simulations using the model, and compare the simulations to the original data. In general, the model appears to capture the main characteristics of the vertical dynamics, except in cases where the data is characterized by a longlasting transient state at the start of the time series. [ABSTRACT FROM AUTHOR]

Brownian motion has been constructed in different ways. Einstein was the most outstanding physicists involved in its construction. From a physical point of view a dynamical theory of Brownian motion was favorable. The Ornstein-Uhlenbeck process models such a dynamical theory and E. Nelson amongst others derived Brownian motion from Ornstein-Uhlenbeck theory via a scaling limit. In this paper we extend the scaling result to α-stable Lévy processes. [ABSTRACT FROM AUTHOR]

The Ornstein-Uhlenbeck neuronal model is reviewed, and estimation of the input parameters from first-passage times are being discussed. Three methods previously suggested in the literature are compared through simulations; namely what we have denoted the Moment Method, the Laplace Transform method, and the Integral Equation method. Finally the methods are also applied to experimental data, where the membrane potential is also recorded intracellularly. This permits to compare the methods based on the limited information contained in first-passage times only to evaluations from more complete observations of the otherwise hidden membrane potential. [ABSTRACT FROM AUTHOR]

We discuss and compare all relativistic stochastic processes existing in the litterature. In particular, the Relativistic Ornstein-Uhlenbeck Process is presented in detail, as is the intrinsic Brownian Motion studied by Franchi and Le Jan. The Relativistic Brownian Motion of Dunkel and Hänggi is also reviewed, together with a model introduced by Oron and Horwitz. We finally suggest some possible future developements of the current research. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]

We revisit the Mason and Weitz (Phys. Rev. Lett., 74, 1995) and Levine and Lubensky (Phys. Rev. Lett., 85, 2000) analysis for one- and two-bead microrheology. Our first motivation is the possibility of drawing inferences from experimental data about local diffusive properties of individual beads and nonlocal dynamic moduli of the medium separating the two beads. Our second motivation is the ability to perform direct numerical simulations of hydrodynamically coupled Brownian beads in soft matter. For both goals, we first must have a model for the coupling between these two transport properties. We reformulate the coupled generalized Langevin equations (GLE) following the scalar GLE analysis of Fricks et al. (J. Appl. Math., 2008), assuming an exponential series parametrization of both local and nonlocal memory kernels. We then show the two-bead GLE model can be represented as a vector Ornstein-Uhlenbeck process, which allows for a fast and statistically accurate numerical simulation of coupled bead paths (time series) and of ensemble-averaged statistics of the process. In this proceedings, we announce the framework to accomplish these two goals of inversion and direct simulation. [ABSTRACT FROM AUTHOR]